It seems to me that if you lost power in a curve, that the bike would tend to fall into the curve.

Try it again only this time try not to provide steering input. I think you will obtain a different result.

How so? If the 'default' is for a bike to go straight under power, but we apply steering to make it turn. Then, when the bike is in the turn gravity is trying to make it fall into the turn but the power applied is balancing that.